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An Old Conjecture Falls, Making Spheres a Lot More Complicated

quantamagazine.org

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Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#4

Post by datavirtue »

The first sentence should have been the ball-is-equal-to-egg explanation with mention of topology. Before that I had no idea what they were talking about.

P.s. I have to assume the rules forbid shapes with surfaces of zero thickness. Otherwise I can just smash a ball into an inner-tube. If the shapes have thickness mandated, what is it? Are the thickness of the surfaces a consideration when morphing from one shape to another? Is the surface thickness negative or positive from zero? All of these questions stem from my experience in 3D modeling where these parameters must be defined.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#5

Post by dullcrisp »

datavirtue wrote: post #4

The first sentence should have been the ball-is-equal-to-egg explanation with mention of topology. Before that I had no idea what they were talking about. P.s. I have to assume the rules forbid shapes with surfaces of zero thickness. Otherwise I can just smash a ball into an inner-tube. If the shapes have thickness mandated, what is it? Are the thickness of the surfaces a consideration when morphing from one shape to…

There is no thickness (or it’s zero if you like). The deformations have to be continuous mathematical functions, so punching a hole isn’t possible.

The study is about the properties of (higher dimensional) shapes rather than concrete objects. It’s like asking what’s the thickness of a circle.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#6

Post by [deleted] »

datavirtue wrote: post #4

The first sentence should have been the ball-is-equal-to-egg explanation with mention of topology. Before that I had no idea what they were talking about. P.s. I have to assume the rules forbid shapes with surfaces of zero thickness. Otherwise I can just smash a ball into an inner-tube. If the shapes have thickness mandated, what is it? Are the thickness of the surfaces a consideration when morphing from one shape to…

[deleted]

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#8

Post by wcarron »

dullcrisp wrote: post #5
datavirtue wrote: post #4

The first sentence should have been the ball-is-equal-to-egg explanation with mention of topology. Before that I had no idea what they were talking about. P.s. I have to assume the rules forbid shapes with surfaces of zero thickness. Otherwise I can just smash a ball into an inner-tube. If the shapes have thickness mandated, what is it? Are the thickness of the surfaces a consideration when morphing from one shape to…

There is no thickness (or it’s zero if you like). The deformations have to be continuous mathematical functions, so punching a hole isn’t possible. The study is about the properties of (higher dimensional) shapes rather than concrete objects. It’s like asking what’s the thickness of a circle.

Easy, it's 0.38mm.

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#9

Post by alan-crowe »

e12e wrote: post #3

I enjoy this way more pretending it's the prelude to a Philip K Dick or H P Lovecraft story - than trying to actually grasp the math :)

If you enjoy the intersection of H P Lovecraft and mathematics you may enjoy https://www.hulver.com/scoop/story/2009/1/15/182727/390

Re: An Old Conjecture Falls, Making Spheres a Lot More Complicated

#10

Post by iraqmtpizza »

do they call them all spheres just to pretend that their work is relevant? I've heard from captain beyond that everything's a circle, but this is one step too far. a 100-dimensional non-uniform egg is not a sphere in any possible way. why is it not called an n-manifold or something like that
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